Note: Please hide solutions. I would like to not see the solution accidentally.

This is exercise 6.1.5. in the Introduction to Algebra book:

Exercise 6.1.5. in the Introduction to Algebra Book wrote:

Alice changes size several times. The ratio of her original height to her second height is 24:5. The ratio of her second height to her third height is 1:12. The ratio of her original height to her fourth height is 16:1. The tallest of these four heights is 10 feet. What is her shortest height? (Source: MATHCOUNTS)

I began by organizing the information. Then I tried to turn it all into one ratio, but I had trouble with 24 and 16. Now that I am writing about that, I don't think that has anything to do with one ratio or three. I don't know how to find, however, the largest height. The larger height is the larger number, right? Or am I wrong? So her original height was larger than her second height, if that was a correct thought process.

My question is: Is the larger number the larger height? Please, just answer that for now. You can solve it, but please hide solutions. With an answer to that, I would be able to solve the rest. Thank you!